On blocking sets of quadrics
A blocking set \(B\) of a quadric \(Q\) with respect to \(s\)-dimensional subspaces is a set of points of \(Q\) such that every \(s\)-dimensional subspace contained in the quadric \(Q\) meets \(B\) in at least one point. A blocking set with respect to lines is simply called blocking set. In the paper under review the three smallest blocking sets with respect to lines of the parabolic quadric \(Q(2n,q)\) \((n\geq 3)\) and the two smallest blocking sets with respect to lines of the hyperbolic quadric \(Q^+(2n+1,q)\) \((n\geq 2)\) are determinated. These blocking sets are obtained intersecting the quadric with a hyperplane; if such a hyperplane is tangent to the quadric, then the intersection is not a minimal blocking set, the pole of \(H\) has to be removed to obtain a minimal blocking set. This result is obtained as a consequence of two theorems regarding blocking sets of upper bounded size in \(Q^+(2n+1,q)\) and \(Q(2n,q)\), respectively.
scientific article; zbMATH DE number 1443435